Happy pi/archetype/ankh day!

[Poffo]

Thanks, guys. What about this, then: "what is 7 circles as the 2d hexagon is actually 8 spheres as a cube; 7 plus the octave."

How do you fit 8 spheres into a cube -- two layers of four?

Exactly!

There are numbers in math called Figurate numbers, and this basically means that a specific number of similar units (like circles or spheres) can be arranged into a specific geometric shape without any left units over or missing. One of the simplest examples of this is the square numbers:

1, 4, 9, 16, 25, 49, ... All are _x_ , 1x1, 2x2, 3x3, ...

The cube numbers then are just the next dimensional level of the squares:

1, 8, 27, 64, 125, 216, ... All are _x_x_ , 1x1x1, 2x2x2, 3x3x3, ...

So the cube of 8 is composed of twice the square number 4, and the Rubik's cube is just a 3x3x3 = 27 micro cubes making up the whole macro cube.

Now, another set of figurates is the Centered Hexagonal, and 7 (as we've already seen) is the second of these:

1, 7, 19, 37, 91, 127, ...

If we bring that 7 (2d hexagon) into 3d it becomes 8. The 8th sphere of the cube is hidden behind the central circle in the 2d hexagonal structure of the seed of life below.:



So if you had a model cube made of 8 smaller cubes (or spheres) and aligned it so it looked like a regular hexagon, you would only see 7 while the 8th would be hidden behind the one directly facing you.

/:idea: